NRHJSur3dq8: a spectral numerical-relativity surrogate family for non-eccentric aligned-spin binary-black-hole waveforms

Abstract: We present NRHJSur3dq8, a family of numerical-relativity (NR) surrogates for non-eccentric aligned-spin binary-black-hole waveforms inspired by an action-angle parameterization. The model provides both the dynamics: the Hamiltonian values, azimuthal action $J_φ(Φ)$, the orbital clock $τ(Φ)$ as functions of its phasing, and the radiative pieces: the waveforms, their near-analytic derivatives, and modeling errors associated with each. The surrogated variables are conditioned into pieces that vary slowly on the radiation-reaction timescale, represented on shared $hp$-adaptive Chebyshev elements, and regressed across the intrinsic parameters with a Gaussian-process model. A time-parameterized merger-ringdown set of elements is attached where the adiabatic description breaks down. Leave-one-out validation of the central NRHJSur3dq8_AA flavor against NR reaches a $(2,2)$ unweighted mismatch of $1.3<sup>{+32}_{-1.2}\times10<sup>{-6}$ and an all-mode mismatch of $2.3<sup>{+59}_{-2.2}\times10<sup>{-6}$ over the full inspiral-merger-ringdown span. Sky-averaged and SNR-weighted over $32$ orientations per simulation, the released model's full-IMR in-sample mismatch against the NR simulations used for training is $8.9\times10<sup>{-7}$ to $2.8\times10<sup>{-5}$ across total masses $40$-$120\,M_\odot$. Waveforms are hybridized using post-Newtonian waveforms. Beyond accuracy, NRHJSur3dq8 provides two capabilities uncommon in NR surrogates: nearly analytic derivatives of the strain with respect to the physical parameters, and a calibrated Gaussian-process predictive uncertainty of the model. A full non-hybridized inspiral-merger-ringdown waveform evaluates in $12$ ms on a single CPU call. Batched evaluation amortizes this to $0.39$ ms per waveform at a batch of $4096$, measured at a starting frequency of $20$ Hz.